218edo: Difference between revisions

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 {{Infobox ET}}
-'''218edo''', having a step size of 5.50458715596 [[cent]]s, contains very accurate ratios, such as [[7/4]], [[9/7]], [[8/7]], [[9/8]], [[10/9]], [[11/10]] and [[17/16]] which are approximated within 0.55&cent; deviation (10% the step size).
+{{EDO intro}}
-The following table shows the nearest matches for the interval, not the matches from the [[patent val]]. '''Bold''' numbers are off within less than 0.1 (10%) of the step size.
+edo is in[[consistent]] to the [[5-odd-limit]], with [[harmonic]] [[3/1|3]] falling about halfway between its steps. However, it contains very accurate ratios, such as [[7/4]], [[9/7]], [[9/8]], [[10/9]], [[11/10]], [[17/16]], and [[19/16]], which are approximated within 0.55-cent deviation (10% the step size). The suggested [[subgroup]]s are therefore 2.9.7.17.19 and 2.9.5.7.11.17.19.23.
-{| class="wikitable"
-|-
-! Interval fraction
-| [[3/2]]
-| [[4/3]]
-| [[5/4]]
-| [[8/5]]
-| [[5/3]]
-| [[6/5]]
-| '''[[7/4]]'''
-| '''[[8/7]]'''
-| [[10/9]]
-| [[9/5]]
-| '''[[9/8]]'''
-| '''[[16/9]]'''
-|-
-! Steps in 218edo
-| 128
-| 90
-| 70
-| 148
-| 161
-| 57
-| '''176'''
-| '''42'''
-| 33
-| 185
-| '''37'''
-| '''181'''
-|}
-Suggested [[subgroup]]s: 2.9.7.17 and 2.9.5.7.11.17.
-Also explore [[436edo]].
 Commas using the [[13-limit]] patent val:
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 ; [[13-limit]]: 28672/28561, 86240/85683, 20480/20449, 5600/5577, 16807/16731, 25000/24843, 6125/6084, 86625/86528, 68992/68445, 58080/57967, 96800/95823, 847/845, 41503/41067, 33275/33124, 65219/64896, 29575/29403, 4225/4224, 21632/21609, 676/675, 33124/32805, 9295/9261, 46475/45927, 13013/12960, 28561/28512
-[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
+=== Odd harmonics ===
+{{Harmonics in equal|218}}
+=== Subsets and supersets ===
+Since 218 factors into {{factorization|218}}, 218edo contains [[2edo]] and [[109edo]] as its subsets. [[436edo]], which doubles it, is worth exploring.